Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)
[tex]x = At^3 + Bt\\m = As^3 + Bs\\m = (\frac{m}{s^3})s^3 + (\frac{m}{s})s[/tex]
Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b) [tex]\frac{dx}{dt} = 3At^2 + B = 3(\frac{m}{s^3})s^2 + \frac{m}{s} = m/s[/tex]
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.
